Gravitational S-matrix from CFT dispersion relations (1711.02031v1)

Abstract: We analyse the double-discontinuities of the four-point correlator of the stress-tensor multiplet in N=4 SYM at large t' Hooft coupling and at order $1/N^4$, as a way to access one-loop effects in the dual supergravity theory. From these singularities we extract CFT-data by using two inversion procedures: one based on a recently proposed Froissart-Gribov inversion integral, and the other based on large spin perturbation theory. Both procedures lead to the same results and are shown to be equivalent more generally. Our computation parallels the standard S-matrix reconstruction via dispersion relations. In a suitable limit, the result of the conformal field theory calculation is compared with the one-loop graviton scattering amplitude in ten-dimensional IIB supergravity in flat space, finding perfect agreement.

Gravitational S-matrix from CFT dispersion relations

The paper "Gravitational S-matrix from CFT dispersion relations" presents an analysis of the double discontinuities in the context of the four-point correlator of the stress-tensor multiplet in $\mathcal{N}=4$ SYM, exploring effects at large t'Hooft coupling and at the order $1/N^4$. The aim is to derive a deeper understanding of one-loop effects in the dual supergravity theory through Conformal Field Theory (CFT) techniques. By employing dispersion relation methodologies in CFT, the authors draw parallels to S-matrix reconstruction in conventional quantum field theory, thereby bridging concepts between quantum gravity and strongly coupled field theories.

Key Contributions and Results

1. Dispersion Relations in CFT: The paper employs Froissart-Gribov inversion integrals and large spin perturbation theory as two primary methods to analyze CFT data from singularity structures. This approach closely mimics the usual S-matrix methodology via dispersion relations, drawing a parallel between bulk unitarity methods in AdS/CFT and traditional unitarity methods in quantum field theory.
2. Equivalence of Methods: The research shows that both the Froissart-Gribov inversion integral and large spin perturbation theory are equivalent for reconstructing the full CFT data from double discontinuities. Both methods confirm the dominant influence of singular double discontinuities caused by protected operators in reconstructing the S-matrix, reinforcing the gauge/gravity duality.
3. One-loop Supergravity Effects: The paper elaborates on how one-loop corrections in AdS${}_5$×S${}_5$ in type IIB supergravity can be captured by CFT methods, with the double discontinuity associated with $\log^2v$ terms providing a pathway for such extractions. The calculated CFT data at order $1/N^4$ aligns remarkably well with the one-loop graviton scattering amplitudes in ten-dimensional supergravity.
4. Flat Space Limit Analysis: Interestingly, the paper explores the limit where CFT correlators encode the flat space S-matrix of type IIB supergravity, specifically focusing on high-dimensional interactions and the magnitude of higher-order corrections. The effective field theory methods used bridge the difference between the AdS and flat space analyses, offering consistency and physical insights into gravity scattering processes.

Implications and Future Work

The findings and methodologies presented have significant implications for both the theoretical and practical understanding of gravity within the framework of AdS/CFT. By consolidating the dispersive methods in CFT as a robust tool for analyzing quantum gravity effects, a substantial foundation is provided for addressing higher or infinite-dimensional operators that might appear in bulk theories. This also opens promising research avenues where the lessons learned from large-N CFTs and gravity duals can be applied to other lower-dimensional or less supersymmetric scenarios, ultimately fostering further advancements in quantum gravity theory.

Looking ahead, the exploration of gravitational S-matrix through well-defined CFT techniques seems poised to unify concepts across different dimensions and supersymmetries, serving as an archetype for similar analyses in other gravity theories. Additionally, the adherence to unitarity and crossing constraints motivates deeper inquiries into nonperturbative regimes of these correspondences, potentially facilitating novel hybrid approaches that merge numerical and analytical techniques in the CFT bootstrap tradition.

With its innovative approach to bridging dispersion relations within the gravity framework, this paper not only aids in decoding complexities within the AdS/CFT correspondence but also enhances the comprehensibility of quantum gravity phenomena in broader and more intricate settings.